Faculty Profiles - MIYAGUCHI Tomoshige

Published Papers - MIYAGUCHI Tomoshige

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Memory-induced slow relaxation in the generalized Langevin equation

Makoto Shimizu, Tomoshige Miyaguchi, Eiji Yamamoto, Takuma Akimoto

The Journal of Chemical Physics 2025.09

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Generalized Langevin dynamics for single beads in linear elastic networks

Soya Shinkai, Shuichi Onami, Tomoshige Miyaguchi

Physical Review E 2024.10

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Generalized Langevin equation with fluctuating diffusivity

Tomoshige Miyaguchi

Physical Review Research 2022.10

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Detrended fluctuation analysis of earthquake data

Takumi Kataoka, Tomoshige Miyaguchi, Takuma Akimoto

Physical Review Research 2021.07

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Piecewise linear model of self-organized hierarchy formation

Tomoshige Miyaguchi, Takamasa Miki, Ryota Hamada

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 102 ( 3 ) 2020.09

The Bonabeau model of self-organized hierarchy formation is studied by using a piecewise linear approximation to the sigmoid function. Simulations of the piecewise-linear agent model show that there exist two-level and three-level hierarchical solutions and that each agent exhibits a transition from nonergodic to ergodic behaviors. Furthermore, by using a mean-field approximation to the agent model, it is analytically shown that there are asymmetric two-level solutions, even though the model equation is symmetric (asymmetry is introduced only through the initial conditions) and that linearly stable and unstable three-level solutions coexist. It is also shown that some of these solutions emerge through supercritical-pitchfork-like bifurcations in invariant subspaces. Existence and stability of the linear hierarchy solution in the mean-field model are also elucidated.

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Reduction of self-diffusion coefficient in a coarse-grained model of cytoplasm

Tomoshige Miyaguchi

PHYSICAL REVIEW RESEARCH ( AMER PHYSICAL SOC ) 2 ( 1 ) 2020.03

Theoretical predictions for polydisperse hard-sphere suspensions with and without hydrodynamic interaction are applied to a coarse-grained model of bacterial cytoplasm, which consists of 15 species of spherical particles. Short-time and long-time self-diffusion coefficients of each species are obtained to the first order in concentration. It is shown that the hydrodynamic interaction leads to a large reduction of diffusivity for small particles such as green fluorescent proteins. Moreover, a heuristic modification of the above theory to make it valid at higher concentrations is presented.

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Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation

Tomoshige Miyaguchi, Takashi Uneyama, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 100 ( 1 ) 2019.07

We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of alternating renewal processes to study a relaxation function which is expressed with an integral of the diffusivity over time. This relaxation function can be related to a position correlation function if the particle is in a harmonic potential and to the self-intermediate scattering function if the potential force is absent. It is theoretically shown that, at short times, the exponential relaxation or the stretched-exponential relaxation are observed depending on the power-law index of the sojourn-time distributions. In contrast, at long times, a power-law decay with an exponential cutoff is observed. The dependencies on the initial ensembles (i.e., equilibrium or nonequilibrium initial ensembles) are also elucidated. These theoretical results are consistent with numerical simulations.

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Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity

Takashi Uneyama, Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 99 ( 3 ) 2019.03

We study the relaxation behavior of the Ornstein-Uhlenbeck (OU) process with time-dependent and fluctuating diffusivity. In this process, the dynamics of the position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions of the transfer matrix for general FD processes. We apply our general theory to two simple FD processes where the FD is described by the Markovian two-state model or an OU-type process. We show analytic expressions of the relaxation functions in these models and their asymptotic forms. We also show that the relaxation behavior of the OU process with an FD is qualitatively different from those obtained from conventional models such as the generalized Langevin equation.

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Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

Tomoshige Miyaguchi

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 96 ( 4 ) 2017.10

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

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Langevin equation with fluctuating diffusivity: A two-state model

Tomoshige Miyaguchi, Takuma Akimoto, Eiji Yamamoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 94 ( 1 ) 2016.07

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

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Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

Takashi Uneyama, Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 92 ( 3 ) 2015.09

The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

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Anomalous diffusion in a quenched-trap model on fractal lattices

Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 91 ( 1 ) 2015.01

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble-and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergodicity breaking. Moreover, time-averaged MSD exhibits aging and converges to a random variable following the modified Mittag-Leffler distribution. It is also shown that the QTM on a fractal lattice cannot be reduced to the continuous-time random walks if the spectral dimension of the fractal lattice is less than 2.

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Phase Diagram in Stored-Energy-Driven Levy Flight

Takuma Akimoto, Tomoshige Miyaguchi

JOURNAL OF STATISTICAL PHYSICS ( SPRINGER ) 157 ( 3 ) 515 - 530 2014.11

Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven L,vy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move while storing energy, and it jumps by the stored energy. The SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion, depending on the coupling parameter between storing time (trapping time) and stored energy. This stochastic process can be investigated analytically with the aid of renewal theory. Here, we consider two different renewal processes, i.e., ordinary renewal process and equilibrium renewal process, when the mean trapping time does not diverge. We analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping-time distribution. In particular, we find that distributional behavior of time-averaged MSD intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge.

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Distributional ergodicity in stored-energy-driven Levy flights

Takuma Akimoto, Tomoshige Miyaguchi

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 87 ( 6 ) 2013.06

We study a class of random walk, the stored-energy-driven Levy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean-square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean-square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

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Ergodic properties of continuous-time random walks: Finite-size effects and ensemble dependences

Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 87 ( 3 ) 2013.03

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e., distributions of the first waiting time). Here, we consider two ensembles: the equilibrium and a typical nonequilibrium ensemble. For both ensembles, it is shown that the time-averaged mean square displacement (TAMSD) exhibits a crossover from normal to anomalous diffusion due to the spatial confinement and this crossover does not vanish even in the long measurement time limit. Moreover, for the nonequilibrium ensemble, we show that the probability density function of the diffusion constant of TAMSD follows the transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a clear transition from weak ergodicity breaking (an irreproducible regime) to ordinary ergodic behavior (a reproducible regime) as the measurement time increases. This convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution; in other words, the weak ergodicity breaking persists for a long time. In addition, it is shown that, aside from the TAMSD, a class of observables also exhibits this slow convergence to ergodicity. We also point out that, even though the system with the equilibrium initial ensemble shows no aging, its behavior is quite similar to that for the nonequilibrium ensemble. DOI: 10.1103/PhysRevE.87.032130

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Crossover time in relative fluctuations characterizes the longest relaxation time of entangled polymers

Takashi Uneyama, Takuma Akimoto, Tomoshige Miyaguchi

JOURNAL OF CHEMICAL PHYSICS ( AMER INST PHYSICS ) 137 ( 11 ) 2012.09

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4752768]

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Ultraslow convergence to ergodicity in transient subdiffusion

Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 83 ( 6 ) 2011.06

We investigate continuous time random walks with truncated alpha-stable trapping times. We prove distributional ergodicity for a class of observables; namely, the time-averaged observables follow the probability density function called the Mittag-Leffler distribution. This distributional ergodic behavior persists for a long time, and thus the convergence to the ordinary ergodicity is considerably slower than in the case in which the trapping-time distribution is given by common distributions. We also find a crossover from the distributional ergodic behavior to the ordinary ergodic behavior.

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Intrinsic randomness of transport coefficient in subdiffusion with static disorder

Tomoshige Miyaguchi, Takuma Akimoto

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 83 ( 3 ) 2011.03

Fluctuations in the time-averaged mean-square displacement for random walks on hypercubic lattices with static disorder are investigated. It is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking. For two-and higher-dimensional systems, the distribution function of the diffusion coefficient is found to be the Mittag-Leffler distribution, which is the same as for the continuous-time random walk, whereas for one-dimensional systems a different distribution (a modified Mittag-Leffler distribution) arises. We also present a comparison of these two distributions in terms of an ergodicity-breaking parameter and show that the modified Mittag-Leffler distribution has a larger deviation from ergodicity. Some remarks on similarities between these results and observations in biological experiments are presented.

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Topology of magnetic field lines: Chaos and bifurcations emerging from two-action systems

Tomoshige Miyaguchi, Makoto Hosoda, Katsuyuki Imagawa, Katsuhiro Nakamura

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 83 ( 1 ) 2011.01

Nonlinear dynamics of magnetic field lines generated by simple electric current elements are investigated. In general, the magnetic field lines show behavior similar to that of the Hamiltonian systems; in fact, they can be generally transformed into Hamiltonian systems with 1.5 degrees of freedom, obey the Kolmogorov-Arnold-Moser (KAM) theorem, and generate chaotic trajectories. In the case where unperturbed systems are described by two action (slow) and one angle (fast) variables, however, it is found that the periodic orbits of the unperturbed systems vanish for arbitrarily small symmetry-breaking perturbations (a breakdown of the KAM theorem) and drifting or periodic trajectories appear. The mechanism of this phenomenon is investigated analytically by weak nonlinear stability analysis. It is also shown numerically that scattering processes of the perturbed system exhibit typical features of chaotic dynamical systems.

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Role of infinite invariant measure in deterministic subdiffusion

Takuma Akimoto, Tomoshige Miyaguchi

PHYSICAL REVIEW E ( AMER PHYSICAL SOC ) 82 ( 3 ) 2010.09

Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time difference is much smaller than the total observation time, the time-averaged mean square displacement depends linearly on the time difference. Furthermore, the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the Mittag-Leffler distribution.

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Published Papers - MIYAGUCHI Tomoshige